A firm produces output using the technology )3 = (1/1000)KL1!'= where capital, K, is measured in machine-hours, labor, L, is measured in person-hours, and y denotes yearly output. The hourly wage rate w = 10, and the hourly rental rate of capital is r = 20. a. (6pts) Does this technology display increasing, constant, or decreasing returns to scale? Please justify. b. (6pts) Compute the marginal products of labor and capital. c. (6pts) Suppose that at the end of 2021 the firm has signed a contract to rent K = 1000 machine-hours over the course of the year 2022. Derive the firm's short run cost function in the year 2022. d. (7pts) What is the firm's short run marginal cost function? What is the firm's short run average cost function? At which point do these two curves intersect